FIG. 1-2 shows a typical multi-carrier communication system MC-SYS using OFDM. A source 1 generates a digital bit stream which is encoded by the channel coder 2. The signal mapper 3 maps the encoded bits output by the channel coder 2 onto n sub-carriers. Thus, the output dn(i) of the signal mapper 3 constitutes the transmitted data symbols mapped onto the subcarrier n. i is the symbol/time index. One of the specific OFDM elements is the transmitter multi-carrier filter bank 4 which carries out an Inverse Fast Fourier Transform IFFT. The outputs of the filter bank 4 are the multi-carrier symbols to be transmitted from the transmitter TR to the receiver RC via a dispersive channel 6. A guard band adjustment unit 5 is provided for introducing a guard interval in order to avoid inter-symbol interference.
On the receiver side RC a removal unit 7 for the guard interval is provided and the receiver multi-carrier filter bank 8 performing a Fast Fourier Transform FFT on the received multi-carrier symbols (from which the guard interval has been removed) outputs the received data symbols. The outputs Xrec,n(i) of the receiver filter bank 8 are the data received on the n-th subcarrier of the i-th OFDM data symbol.
A channel estimator 12 performs an estimation of the channel and the output Cest,n(i) constitutes the channel coefficient of the n-th subcarrier. The channel coefficients are used in a metric calculator 9 to compensate the effects of the dispersive channel in the received data symbols. The decoder 10 performs the channel decoding and a received bit stream is output to the sink 11.
As shown in FIG. 1-2, anywhere between the transmitter filter bank 4 and the receiver filter bank 8 each time domain sample (multi-carrier symbol) may be subject to a frequency offset foff and noise n. Although in FIG. 1-2 the frequency offset and the noise n are illustrated with a multiplier 6′ and an adder 6″ between the channel 6 and the receiver RC units, it may be noted that such frequency offsets and the addition of noise can occur anywhere in the receiver RC and not necessarily only on the actual channel 6 during transmission. In case of a frequency offset foff as schematically illustrated with the multiplier 6′ each time domain sample k is rotated by ejkΔφ, wherein Δφ=2πfoffTs. Ts is the sampling time of the FFT operator in the FFT receiver filter bank 8. Thus, the data received on the n-th subcarrier of the i-th OFDM symbol can be represented as follows:                                           χ                          rec              ,              n                                ⁡                      (            i            )                          =                                                            d                n                            ⁡                              (                i                )                                      ⁢                                          C                n                            ⁡                              (                i                )                                      ⁢                          ⅇ                                                jⅈ                  ⁡                                      (                                          N                      +                      G                                        )                                                  ⁢                Δφ                                      ⁢                          si              ⁡                              (                                  N                  ⁢                                                                          ⁢                                      Δφ                    2                                                  )                                              +                                                                      ICI                  n                                ⁡                                  (                  i                  )                                            +                                                n                  n                                ⁡                                  (                  i                  )                                                                    ︸                                                n                  ′                                ⁢                                  a                  ⁡                                      (                    i                    )                                                                                                          (        1        )                dn(i) transmitted data, mapped onto subcarrier n    Cn(i) channel coefficient on subcarrier n    N number of sub-carriers    G number of samples of guard interval   si  ⁢      (          N      ⁢                          ⁢              Δφ        2              )       damping due to frequency mismatch; for foffNTs<5% it is ≈1 and can thus be neglected here    ICIn(i) intercarrier interference on subcarrier n; its exact value depends on the offset as well as the signals and channel coefficients of all sub-carriers other than n    nn(i) additive noise on subcarrier
The intercarrier interference ICIn(i) and the additive noise nn(i) can be combined to one noise term n′n(i). Thus, the rotationiφ=i(N+G)Δφ  (2)of the received signal depends on the time (symbol) index i only but not on the subcarrier n. This means that the rotation iΦ is the same for all N data signals received within one OFDM symbol. Equation (1) can be rewritten to:Xrec,n(i)=dn(i)Cn(i)ejiφvn(i)ejφn,n(i)  (3)    Vn(i) magnitude of transformed noise n′n(i), depending also on data and channel coefficient    Φn,n(i) equivalently transformed phase of noise n′n(i)
The phase of the received signal Xrec,n(i) is thusφrec,n(i)=φdn(i)+φCn(i)+iΦ+Φn,n(i)  (4)
As can be seen from equation (4) the phase φrec,n(i) of the received signal (per data symbol i) depends on various terms such as the phase of the transmitted data dn(i), the phase of the channel coefficient Cn(i), the phase Φ which is a result of the frequency offset and the phase Φn,n(i) dependent on the noise. A frequency tracking device FTD (as shown with examples in FIGS. 2, 3) must therefore determine a phase estimate Φest(i) which can then be used in a discrete PLL (Phase Locked Loop) tracking scheme in order to cancel out the introduced frequency offset.
For example, in a single carrier system as presented in reference [2] “K.-D. Kammeyer, Nachrichtenübertragung, Stuttgart: B. G. Teubner, second ed., 1996”, when assuming a non-dispersive channel and additive noise, the transmitted single carrier data d(i) (i is again the symbol index) experiences an additive noise n(i) and a phase rotation with iΦ before being received as Xrec(i) (in this case the number of sub-carriers n=1). In this single carrier system the phase of the product of Xrec(i) and the conjugate complex of its decided value ddec* (i) represents the phase estimate Φest(i)
The frequency tracking device FTD therefore always consists of a first part for estimating the frequency offset (the phase estimate) and a second part consisting of the correction of the offset. This is generally only true for single carrier systems but also for multi-carrier systems such as OFDM.
Published Prior Art Documents
Due to its good characteristics in wireless transmission systems, e.g. in mobile radio communication networks, the multi-carrier system OFDM (see the aforementioned reference [1] by J. Bingham or the reference [3] by L. Cimini, “Analysis and Simulation of a Digital Mobile Channel Using Orthogonal Frequency Division Multiplexing,” IEEE Trans. on Communications, vol. COM-33, pp. 665–675, July 1985) has been chosen as the transmission concept in the standardization of the HIPERLAN/2 (High Performance Radio Local Area Network). In contrast to the Digital Audio Broadcasting Standard (DAB), where OFDM is combined with a non-coherent DQPSK signal mapping—the HIPERLAN/2 employs a coherent signal mapping (modulation/demodulation). This allows in principle a better performance for the price of needing a channel estimation and of having to track the frequency in order to correct the frequency offsets. Amongst the various multi-carrier communication techniques as mentioned above OFDM in particular reacts sensitively to frequency deviations as these deviations cause a loss of the subcarrier orthogonality on which the functionality of OFDM is based. As explained above, this results in intercarrier interference (ICI) and a rotation of the signal constellation. The rotation is (for small offsets) without effect if OFDM is used with non-coherent demodulation (note that non-coherent demodulation is always combined with DQPSK).
However, for coherent demodulation (coherent signal mapping) even small offsets prove fatal for long enough transmission bursts because as soon as the accumulated rotation has exceeded the decision grid of the signal constellation a correct data detection is completely impossible. Thus, it is important to implement a precise, little complex frequency tracking which functions in the best case without pilot carriers to avoid additional computational overhead and with it a loss of transmission rate or bandwidth-efficiency.
As the OFDM scheme allows specifically simple approaches in the frequency domain (i.e. following the FFT inside the receiver), various methods have been presented in the published prior art based on an estimation of the frequency offset in the frequency domain only. As already explained above, a typical frequency tracking device comprises two essential parts, namely an evaluator for the frequency offset and a correcter for correcting the offset in the received multi-carrier symbols.
FIG. 2 and FIG. 3 both show examples of frequency tracking devices FTD according to the prior art and comprising an evaluator 14 and correction units 13, 13-1, 13-2. Each of the evaluators 14 determine a frequency deviation estimate foff,est by determining the estimated phase offset Φest(i) in the frequency domain, i.e.foff,est=Φest(i)/(2πi)  (5)
Any evaluation algorithm used in the evaluator 14 exploits several values of one OFDM symbol by either averaging over the arguments or by generating the argument of the correlation. The evaluation algorithms for determining Φest(i) can be distinguished by that they are decision directed or pilot aided. The pilot aided methods always have the disadvantage of an additional overhead since less user data can be transmitted.
A first example being decision directed is based on a comparison of the arguments of the received data symbols Xrec,n(i) with their decided data symbol ddec,n(i) and the channel coefficient Cest,n(i). For each OFDM symbol the result is averaged over all used sub-carriers Nused. That is, for each OFDM symbol i the phase estimate can be calculated as:                                           Φ                          est              ,              1                                ⁡                      (            i            )                          =                              1                          N              used                                ⁢                                    ∑                              n                =                0                                                              N                  used                                -                1                                      ⁢                          arg              ⁢                              {                                                                            x                                              rec                        ,                        n                                                              ⁡                                          (                      i                      )                                                        ⁢                                      (                                                                                            d                                                      dec                            ,                            n                                                                          ⁡                                                  (                          i                          )                                                                    ⁢                                                                        C                                                      est                            ,                            n                                                                          ⁡                                                  (                          i                          )                                                                                      )                                    *                                }                                                                        (        6        )            
As in the case of the single carrier system mentioned above the phase estimate Φest,1(i) is the average product of the received symbol and the conjugate complex of its decided values corrected by the channel coefficient. Such type of phase estimate Φest,1(i) is discussed in EP 0 453 203 and EP 6 567 06.
It should be noted that some of the published prior art documents have not explicitly included the channel coefficients for the evaluation of the phase estimate. The received data is equalized beforehand. Nonetheless, all of these evaluation algorithms require the knowledge of the channel coefficients in frequency selective environments, meaning that the channel estimation (which is necessary anyway in the case of coherent signal mapping) has to be performed before the frequency deviation evaluation. In the further description the channel estimate is assumed known and the aforementioned reference [1] gives an example of how the channel coefficients can be determined.
A second example to determine the phase estimate Φest,2(i) is a correlation of the received data of all sub-carriers with the decided data and the channel coefficients of all (used) sub-carriers. This second type of phase estimate can be calculated in accordance with the following equation:                                           Φ                          est              ,              2                                ⁡                      (            i            )                          =                  {                                    ∑                              n                =                0                                                              N                  used                                -                1                                      ⁢                                                            x                                      rec                    ,                    n                                                  ⁡                                  (                  i                  )                                            ⁢                              (                                                                            d                                              dec                        ,                        n                                                              ⁡                                          (                      i                      )                                                        ⁢                                                            C                                              est                        ,                        n                                                              ⁡                                          (                      i                      )                                                                      )                            *                                }                                    (        7        )            
In contrast to equation (6), the second example of the phase estimate in accordance with equation (7) does not sum up the arguments of the received data multiplied with the channel estimate corrected decided data but it is based on taking the argument of the summed up (summed up over the number of used sub-carriers) of the received data multiplied with the channel coefficient corrected decided data.
A third example for determining a phase estimate Φest,3(i) uses received pilot data together with the channel coefficients and the sent pilot data. For one OFDM symbol the result is averaged over all pilot carriers Npilot of that symbol. The third example of the phase estimate is calculated in accordance with the following equation:                                           Φ                          est              ,              3                                ⁡                      (            i            )                          =                              1                          N              pilot                                ⁢                                    ∑                              n                =                0                                                              N                  pilot                                -                1                                      ⁢                          arg              ⁢                              {                                                                            x                                              rec                        ,                        n                                                              ⁡                                          (                      i                      )                                                        ⁢                                      (                                                                                            p                          n                                                ⁡                                                  (                          i                          )                                                                    ⁢                                                                        C                                                      est                            ,                            n                                                                          ⁡                                                  (                          i                          )                                                                                      )                                    *                                }                                                                        (        8        )            where pn(i) is the pilot symbol on the n-th pilot symbol carrying subcarrier.
The following fourth example of a phase estimate Φest,4(i) is using the received pilot data in a correlation with the channel coefficient and the sent pilot data, similarly as was done for the data symbol evaluation in equation (7). That is, a correlation of the received pilot data with the channel coefficient and the sent pilot data can be calculated in accordance with the following equation:                                           Φ                          est              ,              4                                ⁡                      (            i            )                          =                  arg          ⁢                      {                                          ∑                                  n                  =                  0                                                                      N                    pilot                                    -                  1                                            ⁢                                                                    x                                          rec                      ,                      n                                                        ⁡                                      (                    i                    )                                                  ⁢                                  (                                                                                    p                        n                                            ⁡                                              (                        i                        )                                                              ⁢                                                                  C                                                  est                          ,                          n                                                                    ⁡                                              (                        i                        )                                                                              )                                *                                      }                                              (        9        )            
Each of the following publications use either the third or fourth example for determining the phase estimate: EP 6 835 76; EP 7 856 45; DE 197 218 64; GB 2 319 703; DE 197 530 84; and EP 8 174 18.
To simplify the implementation all “arg(x)”-functional expressions can (in case of small frequency offsets) be replaced by simply using the imaginary part Imag (x).
Any of the aforementioned four examples in equations (6)–(9) can be used in the evaluators arranged as shown in FIG. 2, FIG. 3. In case of using a decision directed frequency estimation N in FIGS. 2, 3 denotes the number of used sub-carriers Nused and in case of pilot aided phase determination N denotes the number of used pilot carriers Npilot.
FIG. 2 shows a first example of a correction unit 13 arranged upstream of the receiver multi-carrier filter bank 8. On the basis of the frequency deviation estimate foff,est determined by using equation (5) and the sample index (k) within the multi-carrier symbol each received multi-carrier symbol is rotated with a different phase shift. That is, in FIG. 2 the correction of the offset is performed in a feedback loop before the FFT unit 8. Such type of correction is used in the aforementioned patent documents. In fact, this type of correction is a straightforward rotation of each incoming sample of the i-th multi-carrier symbol with a value which has been obtained from the offset estimates of the symbols at an adjustment time interval before. That is, since the multi-carrier symbols evaluator 14 operates on the set of multi-carrier symbols received at a last symbol duration and the correction with the frequency offset estimation foff,est is carried out on the next set of arriving multi-carrier symbols.
FIG. 3 shows a further example of a corrector which uses instead of the correction unit 13 in FIG. 2 or in addition to the correction unit 13 in FIG. 2 a correction unit 13-2 arranged downstream of the receiver multi-carrier filter bank 8. A system as in FIG. 3 is for example disclosed in reference [4] “Multiträgerkonzepte für die digitale, terrestrische Hörerrundfunk-Übertragung” by Ulrich Tuifel; PhD, Thesis at the Technical University Hamburg-Harburg, February 1993. Arranging the correction unit 13-2 downstream of the receiver multi-carrier filter bank 8 all data symbols output by the multi-carrier filter bank are rotated with the same phase shift depending on frequency deviation estimate foff,est. However, although in the correction unit 13-2 the samples of the i-th symbols are corrected with the value which is derived from the frequency offset estimate of the previous symbols. In contrast to the correction unit 13-1, where each sample of one symbol is corrected with a different incremented value, the correction unit 13-2 rotates each sample of one symbol with the same value. In FIGS. 2, 3 it should be noted that the frequency tracking device FDD includes all units shown with the exception of the multi-carrier filter bank 8.
Disadvantages of the Published Prior Art
As can be seen from equations (6), (8), the phase estimates Φest,1 and Φest,3 are based on the summing up of the arguments of the received data with their decided data corrected by the channel coefficients (8) Xrec,n(i) denotes the received pilot data on the n-th sub-carrier of the i-th symbol. Since the first and third examples of the phase estimates therefore do not process probability information, in frequency selective environments the data transmitted on the sub-carriers with small channel coefficients (where noise badly distorts the received signal), is equally weighted as the data on sub-carriers with large channel coefficients, where the influence of the noise is small and where thus, in case of the example 1, false decisions are less likely. Since the second and fourth phase estimates are based on a processing of probability information and inherently weight the sub-carriers with the channel coefficients, the performance can be improved. Although sub-carriers with small channel coefficients are not weighted as much, they can distort the phase estimate due to false decisions in case of a decision directed approach in the second example.
In case of the pilot aided third and fourth examples, the number of pilot carriers has to be chosen large enough to ensure a good averaging process and with it a good estimate. Due to the large number of pilot carriers necessary to obtain a good averaging process the computational overhead is undesirably increased.
Another disadvantage, already mentioned above, is that the correction performed in FIG. 2 and FIG. 3 is time-shifted (delayed), meaning that the evaluation data of one symbol i is used to correct the data of the next symbol i+1 (or that the actual symbol i is corrected with a value from the previous estimate i−1). This results in a residual error which degrades the performance.